# Flume Experiments for Optimizing the Hydraulic Performance of a Deep-Water Wetland Utilizing Emergent Vegetation and Obstructions

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Study Area

#### 2.2. Flume Experiment Setup

#### 2.2.1. Physical Model

_{m}is the length of the model, L

_{p}is the length of the prototype, A

_{m}is the area of the model, A

_{p}is the area of the prototype, and λ

_{L}is a scale factor for the length.

_{m}is the velocity of the model fluid; v

_{p}is the velocity of the prototype fluid; Q

_{m}is the discharge of the model; Q

_{p}is the discharge of the prototype; L

_{m}is the length of the model; L

_{p}is the length of the prototype; T

_{m}is the time when observing the model; T

_{p}is the time when observing the prototype; and λ

_{L}, λ

_{T}, λ

_{v}, and λ

_{Q}are scale factors for the length, time, velocity, and discharge.

_{m}is the force of the model fluid; F

_{p}is the force of the prototype fluid; M

_{m}is the mass of the model fluid; M

_{p}is the mass of the prototype fluid; a

_{m}is the acceleration of the model fluid; a

_{p}is the acceleration of the prototype fluid; ρ

_{m}is the density of the model fluid; ρ

_{p}is the density of the prototype fluid; L

_{m}is the length of the model; L

_{p}is the length of the prototype; and λ

_{ρ}, λ

_{L}, λ

_{T}, λ

_{v}, and λ

_{F}are scale factors for the density, length, time, velocity, and force.

_{m}is the Reynolds number of the model fluid, Re

_{p}is the Reynolds number of the prototype fluid, ρ

_{m}is the density of the model fluid, ρ

_{p}is the density of the prototype fluid, v

_{m}is the velocity of the model fluid, v

_{p}is the velocity of the prototype fluid, L

_{m}is the length of the model, L

_{p}is the length of the prototype, μ

_{m}is the dynamic viscosity of the model fluid, and μ

_{p}is the dynamic viscosity of the prototype fluid.

_{m}= μ

_{p}and ρ

_{m}= ρ

_{p}. All geometric and kinematic parameters were made equivalent, and corresponding angles of the prototype wetland and experimental flume were the same. We developed the experimental flume with a true model (not distorted) to avoid scale effects [13]. Thus, λ

_{v}= 1/λ

_{L}, λ

_{T}= λ

_{L}

^{2}and λ

_{Q}= λ

_{L}by substituting Equation (6) into Equations (3) and (4). The model-to-prototype ratios of length, time, velocity, and discharge were determined to be 1/25, 1/625, 25, and 1/25, respectively (Table 1). The prototype measured 50 m wide by 75 m long (Figure 1b), the water level downstream was controlled at 2 m, and the discharge was set at 0.01 m

^{3}/s. Therefore, the flume model was 2 m wide by 3 m long (Figure 1c), the water level was 8 cm, and the discharge was 0.0004 m

^{3}/s.

#### 2.2.2. Obstructions and Emergent Vegetation

#### 2.2.3. Tracer and Detector

_{out}is the mass of tracer at the outlet, Q is the discharge, C is the tracer concentration, t is the time of measurement, and T is the total time of the tracer experiment.

#### 2.3. Residence Time, Effective Volume, and Hydraulic Efficiency

_{n}; Equation (8)), and using the residence time distribution (RTD) method, which yields the mean residence time (t

_{m}; Equation (9)) [8]. The HRT was calculated by assuming an aquatic system with uniform, unrestricted water flow with no mixing and/or diffusion and a nominal retention time [16]. The RTD method is used to assess the mixing, diffusion, and RTD of a fluid in a reactor vessel; it models the flow conditions of a fluid in a reactor better than does the HRT method [17].

_{n}is the nominal retention time.

_{m}is the mean residence time.

_{v}indicates the effective volume ratio of a detention system based on the ratio of t

_{m}to t

_{n}as per Equation (10) [18].

_{m}is the mean residence time, t

_{n}is the nominal retention time, and e

_{v}is the effective volume ratio.

_{p}is the time of the peak concentration in the RTD curve measured at the outlet of the wetland or facility, t

_{m}is the mean residence time, t

_{n}is the nominal retention time, and λ is the hydraulic efficiency.

## 3. Results and Discussion

#### 3.1. No Obstructions or Vegetation

_{n}), mean residence time (t

_{m}), effective volume (e

_{v}) and hydraulic efficiency (λ) were calculated and are shown in Table 3. The hydraulic efficiency was classified as poor. The following tests were set up with internal obstructions and emergent vegetation.

#### 3.2. Installation of Obstructions

_{n}) decreased linearly with increases in the obstruction volume. The mean residence time (t

_{m}) appeared to increase with increases in the quantity and length of obstructions. Although the volume percentage corresponding to the case with high aspect ratios was rather high, t

_{m}did not significantly increase. The effective volume (${e}_{v}$) increased with increases in the obstruction volume (Table 3). In the cases with low aspect ratios (cases 1-1, 1-2, 1-3, 2-1, 2-2, 2-3, 3-1, 3-2, 3-3), the hydraulic efficiency (λ) improved significantly when the number and lengths of obstructions were increased. Among all of the configurations, the group consisting of cases 3-1, 3-2, and 3-3 yielded the largest improvements in λ. Case 3-3 exhibited a λ of 0.87, i.e., good hydraulic efficiency. Cases 1-1, 1-2, and 1-3 yielded the second largest improvement in λ. Cases 2-1, 2-2, and 2-3 yielded the smallest improvements in λ, and only case 2-3 yielded satisfactory hydraulic efficiency. Among the cases with high aspect ratios, i.e., cases 2-4, 2-5 and 2-6, none of the λ values improved significantly; all yielded poor hydraulic efficiency. After installing the high-aspect-ratio EOs, we observed constrained water conveyance and a distinct short-circuited flow, i.e., an area with relatively high flow velocity. The short-circuited flow reduced the residence time and flow uniformity and thereby decreased the hydraulic performance and treatment efficiency.

_{n}) decreased linearly with increases in the obstruction volume. In the cases with low aspect ratios, the mean residence time (t

_{m}) increased with increases in the number and lengths of obstructions (Table 4). In the cases with high aspect ratios, although the volume percentage was somewhat higher, the effective volume (${e}_{v}$) increased with increases in the obstruction volume (Figure 4a). In the cases with low aspect ratios, the hydraulic efficiency (λ) increased as the number and lengths of obstructions increased, although, this effect was not highly significant (Figure 4b). The majority of the λ values were less than 0.75, representing poor hydraulic efficiency. The nominal retention time (t

_{n}) decreased linearly with increases in the obstruction volume. In the cases with low aspect ratios, the EOs yielded significantly greater improvements in hydraulic efficiency (λ) than did the SOs (Figure 4). In contrast, in the cases with high aspect ratios, the EOs yielded less improvement than did the SOs. The high-aspect-ratio EOs clearly altered the flow direction and constrained the water conveyance area more than did the low-aspect-ratio EOs, and this greater alteration may have caused the short-circuited flow. The short-circuited flow occurred in the areas with relatively high flow speeds, caused by lower friction and constrained conveyance water area. This creates a non-uniform flow condition, resulting in a decrease in the residence time and hydraulic efficiency, which also prevents a wetland from improving the water quality.

#### 3.3. Installation of Emergent Vegetation

_{n}) associated with the HEV decreased linearly with increases in the obstruction volume. The mean residence time (t

_{m}) increased with increases in the quantities and lengths of the emergent vegetation installations (Table 5). The effective volume (${e}_{v}$) increased with increases in the volumes of the emergent vegetation (Figure 5a). In the cases with low aspect ratios, the hydraulic efficiency (λ) increased with increases in the lengths of the emergent vegetation installations and with increases in the quantity of the emergent vegetation (Figure 5b). In cases 3-1, 3-2, and 3-3, λ increased to 0.75 or more, representing good hydraulic efficiency. In the cases with high aspect ratios, λ increased with increases in the lengths of the emergent vegetation installations on both sides. However, the improvement in efficiency was less significant than that associated with the low aspect ratios; λ reached a value of 0.5 or higher, representing satisfactory hydraulic efficiency.

_{n}) associated with the LEV decreased linearly with increases in the volume of the emergent vegetation. The mean residence time (t

_{m}) increased with increases in the quantity and lengths of the emergent vegetation installations. The effective volume (${e}_{v}$) increased with increases in the volume of the emergent vegetation (Table 6). In the cases with low aspect ratios, the hydraulic efficiency (λ) increased with increases in the lengths of the emergent vegetation installations. λ exhibited a clear increase with increases in the quantity of emergent vegetation. In cases 3-2 and 3-3, λ increased to 0.75 or greater, representing good hydraulic efficiency. The quantity of high-aspect-ratio emergent vegetation (cases 2-4, 2-5 and 2-6) was positively correlated with the hydraulic efficiency regardless of whether the vegetation consisted of HEV or LEV. In the cases with high aspect ratios, λ increased with increases in the lengths of the emergent vegetation installations on both sides. However, the improvement in efficiency was less significant than that associated with the low aspect ratios; λ reached 0.5 or more, representing satisfactory hydraulic efficiency. Furthermore, the HEV increased the hydraulic efficiency more than did the LEV. The differences between the increases in λ were larger when the quantity of simulated vegetation was low and were smaller when the quantity of simulated vegetation was high.

#### 3.4. Optimization of Hydraulic Performance

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Study area location in Taoyuan County, Northern Taiwan; (

**b**) farm pond (prototype) with dimensions of 50 m wide by 75 m long. The vegetation in the wetland consists of dominant emergent vegetation such as Cyperus papyrus and Cyperus malaccensis Lam. subsp. monophyllus and minor floating vegetation, such as Nuphar shimadai; and (

**c**) flume model of the deep area (2 m wide by 3 m long) viewed from above (

**left**) and a photograph of the flume and the distribution of the installed obstructions in a perspective view from the outlet (

**right**).

**Figure 2.**(

**a**) Sizes and placement of emergent obstructions (EOs), submerged obstructions (SOs), and high- and low-density emergent vegetation (EV) in the side view. The heights of the EOs and SOs are 11 cm and 5 cm, respectively, which yield a protrusion and submergence of 3 cm above and below the water surface, respectively. The emergent vegetation was erected on the SOs and protruded above the water surface; and (

**b**) configuration and dimensions of obstructions. In cases 2-4, 2-5, and 2-6 (high aspect ratio), the obstructions were 120 cm long by 20–60 cm wide. In the other cases (low aspect ratio), the obstructions were 40–120 cm long by 10 cm wide.

**Figure 4.**(

**a**) Effective volumes and (

**b**) hydraulic efficiencies associated with emergent and submerged obstructions.

**Figure 5.**(

**a**) Effective volumes and (

**b**) hydraulic efficiencies associated with low- and high-density emergent vegetation.

**Figure 6.**Hydraulic performance of (

**a**) low-aspect-ratio cases 1-1, 1-2, and 1-3; (

**b**) low-aspect-ratio cases 2-1, 2-2, and 2-3; (

**c**) low-aspect-ratio cases 3-1, 3-2, and 3-3; and (

**d**) high-aspect-ratio cases 2-4, 2-5, and 2-6 with emergent obstructions, submerged obstructions, and high- and low-density emergent vegetation.

Scale Factors | Proportion (Model/Prototype) |
---|---|

Length (λ_{L}) | 1/25 |

Time (λ_{T}) | 1/625 |

Velocity (λ_{v}) | 25 |

Discharge (λ_{Q}) | 1/25 |

**Table 2.**Validation of the flume model based on comparisons with the on-site investigation and mathematical model simulation with no obstructions.

Data Source | t_{n} | t_{m} | t_{p} | e_{v} | λ | Hydraulic Performance ^{4} |
---|---|---|---|---|---|---|

Flume experiment ^{1} | 21.87 min | 14.57 min | 4.7 min | 0.66 | 0.22 | Poor |

Field investigation ^{2} | 239.58 h | 134.24 h | 76.5 h | 0.56 | 0.32 | Poor |

Mathematical model simulation ^{3} | 239.58 h | 135.8 h | 66.5 h | 0.57 | 0.28 | Poor |

**Table 3.**Nominal retention time, mean residence time, peak time, effective volume, and hydraulic efficiency of cases with emergent obstructions.

Cases | t_{n} (min) | t_{m} (min) | t_{p} (min) | e_{v} | λ | Hydraulic Performance | |
---|---|---|---|---|---|---|---|

Low aspect ratio | 1–1 | 21.6 | 16.6 | 8.4 | 0.77 | 0.48 | Poor |

1–2 | 21.3 | 16.9 | 9.8 | 0.79 | 0.56 | Satisfied | |

1–3 | 21.1 | 17.1 | 11.4 | 0.81 | 0.65 | Satisfied | |

2–1 | 21.3 | 16.6 | 6.1 | 0.78 | 0.35 | Poor | |

2–2 | 20.8 | 16.8 | 7.2 | 0.81 | 0.41 | Poor | |

2–3 | 20.3 | 16.9 | 9.1 | 0.83 | 0.52 | Satisfied | |

3–1 | 21.1 | 16.7 | 7.6 | 0.79 | 0.43 | Poor | |

3–2 | 20.3 | 16.9 | 10.0 | 0.83 | 0.57 | Satisfied | |

3–3 | 19.5 | 17.5 | 15.2 | 0.9 | 0.87 | Good | |

High aspect ratio | 2–4 | 20.3 | 16.4 | 5.0 | 0.81 | 0.29 | Poor |

2–5 | 18.7 | 16.6 | 4.8 | 0.89 | 0.27 | Poor | |

2–6 | 17.1 | 16.7 | 5.1 | 0.98 | 0.29 | Poor |

**Table 4.**Nominal retention time, mean residence time, peak time, effective volume, and hydraulic efficiency of cases with submerged obstructions.

Cases | t_{n} (min) | t_{m} (min) | t_{p} (min) | e_{v} | λ | Hydraulic Performance | |
---|---|---|---|---|---|---|---|

Low aspect ratio | 1-1 | 21.7 | 16.3 | 5.1 | 0.75 | 0.29 | Poor |

1-2 | 21.6 | 16.5 | 5.7 | 0.76 | 0.33 | Poor | |

1-3 | 21.5 | 16.6 | 7.3 | 0.77 | 0.42 | Poor | |

2-1 | 21.6 | 16.2 | 4.4 | 0.75 | 0.25 | Poor | |

2-2 | 21.3 | 16.6 | 6.6 | 0.78 | 0.38 | Poor | |

2-3 | 21.1 | 16.7 | 8.0 | 0.79 | 0.46 | Poor | |

3-1 | 21.5 | 16.5 | 6.4 | 0.77 | 0.37 | Poor | |

3-2 | 21.1 | 16.8 | 6.6 | 0.80 | 0.38 | Poor | |

3-3 | 20.7 | 17.0 | 12.9 | 0.82 | 0.74 | Satisfactory | |

High aspect ratio | 2-4 | 21.1 | 16.8 | 5.5 | 0.8 | 0.31 | Poor |

2-5 | 20.3 | 17.2 | 7.2 | 0.85 | 0.41 | Poor | |

2-6 | 19.5 | 17.5 | 8.1 | 0.90 | 0.49 | Poor |

**Table 5.**Nominal retention time, mean residence time, peak time, effective volume, and hydraulic efficiency of cases with high-density emergent vegetation.

Cases | t_{n} (min) | t_{m} (min) | t_{p} (min) | e_{v} | λ | Hydraulic Performance | |
---|---|---|---|---|---|---|---|

Low aspect ratio | 1-1 | 21.7 | 16.6 | 8.5 | 0.76 | 0.49 | Poor |

1-2 | 21.6 | 16.5 | 7.3 | 0.76 | 0.42 | Poor | |

1-3 | 21.5 | 16.8 | 9.8 | 0.78 | 0.57 | Satisfactory | |

2-1 | 21.6 | 16.7 | 5.7 | 0.77 | 0.33 | Poor | |

2-2 | 21.3 | 17.1 | 8.6 | 0.8 | 0.49 | Poor | |

2-3 | 21.1 | 17.5 | 11.7 | 0.83 | 0.65 | Satisfactory | |

3-1 | 21.5 | 17.1 | 14.3 | 0.8 | 0.82 | Good | |

3-2 | 21.1 | 17.6 | 22 | 0.83 | 1 | Good | |

3-3 | 20.7 | 17.9 | 21.2 | 0.87 | 1 | Good | |

High aspect ratio | 2-4 | 21.1 | 17 | 5.6 | 0.81 | 0.32 | Poor |

2-5 | 20.3 | 17.8 | 10.2 | 0.88 | 0.58 | Satisfactory | |

2-6 | 19.5 | 17.9 | 12.5 | 0.92 | 0.71 | Satisfactory |

**Table 6.**Nominal retention time, mean residence time, peak time, effective volume, and hydraulic efficiency of cases with low-density emergent vegetation.

Cases | t_{n} (min) | t_{m} (min) | t_{p} (min) | e_{v} | λ | Hydraulic Performance | |
---|---|---|---|---|---|---|---|

Low aspect ratio | 1-1 | 21.7 | 16.4 | 4.8 | 0.75 | 0.27 | Poor |

1-2 | 21.6 | 16.5 | 5.5 | 0.76 | 0.31 | Poor | |

1-3 | 21.5 | 16.7 | 7.6 | 0.78 | 0.43 | Poor | |

2-1 | 21.6 | 16.6 | 5.0 | 0.77 | 0.28 | Poor | |

2-2 | 21.3 | 16.8 | 6.4 | 0.79 | 0.36 | Poor | |

2-3 | 21.1 | 16.9 | 10.3 | 0.80 | 0.59 | Satisfactory | |

3-1 | 21.5 | 17.0 | 13.2 | 0.79 | 0.75 | Good | |

3-2 | 21.1 | 17.4 | 21.4 | 0.83 | 1.00 | Good | |

3-3 | 20.7 | 17.6 | 18.1 | 0.85 | 1.00 | Good | |

High aspect ratio | 2-4 | 21.1 | 16.8 | 5.8 | 0.80 | 0.33 | Poor |

2-5 | 20.3 | 17.1 | 8.6 | 0.84 | 0.49 | Poor | |

2-6 | 19.5 | 17.2 | 12.2 | 0.88 | 0.70 | Satisfactory |

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**MDPI and ACS Style**

Shih, S.-S.; Hong, S.-S.; Chang, T.-J.
Flume Experiments for Optimizing the Hydraulic Performance of a Deep-Water Wetland Utilizing Emergent Vegetation and Obstructions. *Water* **2016**, *8*, 265.
https://doi.org/10.3390/w8060265

**AMA Style**

Shih S-S, Hong S-S, Chang T-J.
Flume Experiments for Optimizing the Hydraulic Performance of a Deep-Water Wetland Utilizing Emergent Vegetation and Obstructions. *Water*. 2016; 8(6):265.
https://doi.org/10.3390/w8060265

**Chicago/Turabian Style**

Shih, Shang-Shu, Shang-Shang Hong, and Tsang-Jung Chang.
2016. "Flume Experiments for Optimizing the Hydraulic Performance of a Deep-Water Wetland Utilizing Emergent Vegetation and Obstructions" *Water* 8, no. 6: 265.
https://doi.org/10.3390/w8060265